102f05mt2 - B U Department of Mathematics Math 102 Calculus...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
B U Department of Mathematics Math 102 Calculus II Fall 2005 Second Midterm This archive is a property of Bo˘ gazi¸ci University Mathematics Department. The purpose of this archive is to organise and centralise the distribution of the exam questions and their solutions. This archive is a non-profit service and it must remain so. Do not let anyone sell and do not buy this archive, or any portion of it. Reproduction or distribution of this archive, or any portion of it, without non-profit purpose may result in severe civil and criminal penalties. 1. Find the derivative of f ( x, y, z ) = x 3 + y 3 z at ( - 1 , 2 , 1) in the direction toward (0,3,3). Solution: A vector in the indicated direction is (0 , 3 , 3) - ( - 1 , 2 , 1) = < 1 , 1 , 2 > . The unit vector in that direction is ~u = 1 6 < 1 , 1 , 2 > ~ O f ( x, y, z ) = < 3 x 2 , 3 y 2 z, y 3 > ~ O f ( - 1 , 2 , 1) = < 3 , 12 , 8 > Hence, the derivative of f ( x, y, z ) = x 3 + y 3 z at ( - 1 , 2 , 1) in the direction toward (0,3,3) is
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/30/2008 for the course C CMPE 150 taught by Professor Tuna during the Spring '08 term at Boğaziçi University.

Page1 / 3

102f05mt2 - B U Department of Mathematics Math 102 Calculus...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online